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We propose a new data analysis approach for the efficient post-processing of bundles of finite element data from numerical simulations. The approach is based on the mathematical principles of symmetry. We consider the case where simulations…
We describe a family of iterative algorithms that involve the repeated execution of discrete and inverse discrete Fourier transforms. One interesting member of this family is motivated by the discrete Fourier transform uncertainty principle…
Flow of molecular gas into a complex vacuum system is investigated by a lumped parameter model to estimate the time evolution of gas pressure $p_g$, which for the first time takes into account the realistic effect of time-delay arising due…
Discrete gradient methods are a class of numerical integrators producing solutions with exact preservation of first integrals of ordinary differential equations. In this paper, we apply order theory combined with the symmetrized Itoh--Abe…
An inverse problem in spectroscopy is considered. The objective is to restore the discrete spectrum from observed spectrum data, taking into account the spectrometer's line spread function. The problem is reduced to solution of a system of…
Bayesian inference on non-Gaussian data is often non-analytic and requires computationally expensive approximations such as sampling or variational inference. We propose an approximate inference framework primarily designed to be…
The purpose of this paper is to propose a semi-analytical technique convenient for numerical approximation of solutions of the initial value problem for $p$-dimensional delayed and neutral differential systems with constant, proportional…
In this paper we analyse and improve integer discrete flows for lossless compression. Integer discrete flows are a recently proposed class of models that learn invertible transformations for integer-valued random variables. Their discrete…
In this paper will be presented methodology of encoding information in valuations of discrete lattice with some translational invariant constrains in asymptotically optimal way. The method is based on finding statistical description of such…
This study presents the design, discretization and implementation of the continuous-time linear-quadratic model predictive control (CT-LMPC). The control model of the CT-LMPC is parameterized as transfer functions with time delays, and they…
Highly accurate simulations of problems including second derivatives on complex geometries are of primary interest in academia and industry. Consider for example the Navier-Stokes equations or wave propagation problems of acoustic or…
This paper develops and implements a practical simulation-based method for estimating dynamic discrete choice models. The method, which can accommodate lagged dependent variables, serially correlated errors, unobserved variables, and many…
We show that an "old dog", the classical discrete Laplace (aka.~geometric) mechanism, can "perform new tricks": 1. It can be post-processed to yield a simple, unbiased estimator of any subexponential function $f$ of the original data,…
We prove simple general formulas for expectations of functions of a random walk and its running extremum. Under additional conditions, we derive analytical formulas using the inverse $Z$-transform, the Fourier/Laplace inversion and…
This paper presents some applications of using recently developed algorithms for smooth-continuous data reconstruction based on the digital-discrete method. The classical discrete method for data reconstruction is based on domain…
In this short note, we present few results on the use of the discrete Laplace transform in solving first and second order initial value problems of discrete differential equations.
Level-sensitive latches are widely used in high- performance designs. For such circuits efficient statistical timing analysis algorithms are needed to take increasing process vari- ations into account. But existing methods solving this…
This paper discusses the error and cost aspects of ill-posed integral equations when given discrete noisy point evaluations on a fine grid. Standard solution methods usually employ discretization schemes that are directly induced by the…
We propose a general strategy to discretize the Dyson series without applying direct numerical quadrature to high-dimensional integrals, and extend this framework to open quantum systems. The resulting discretization can also be interpreted…
In the post-industrial world, data science and analytics have gained paramount importance regarding digital data privacy. Improper methods of establishing privacy for accessible datasets can compromise large amounts of user data even if the…